Cost-efficiency in the patient centered medical home model: New evidence from federally qualified health centers

Abstract

This research analyzes the cost-efficiency of the Patient Centered Medical Home (PCMH) model vis-à-vis the traditional care delivery model in the Federally Qualified Health Centers (FQHC). We apply the three-stage least squares modeling approach on 2014 UDS data on all FQHCs to estimate per-visit and per-patient cost functions. Log-quadratic and linear-quadratic functional forms of cost are used for the analysis. The estimated models reveal substantial scale economies and cost advantages associated with PCMH status. Aggregate cost-saving impact of PCMH across all FQHCs in 2014 is estimated to be $1.05 billion. Simulations reveal that the PCMH impact on cost savings grows with the size of the patient population. Reaching the full cost-saving potential in PCMH-recognized FQHCs hinges on expanding the health workforce at all levels of care to meet the need of the growing patient population due to aging and Medicaid expansion. For FQHCs that are not PCMH-recognized, capacity/infrastructural expansion appears to be the immediate policy choice.

Appendix

Modeling framework

The practice establishments, because of their large sizes, locational advantages, better access to financial support for infrastructure development, or their leaderships’ motivation to improve quality and reduce costs may be more likely to implement PCMH capabilities. This is true in the case of FQHCs, since only a fraction of the health centers have competed and participated in the demonstration project. Some of the traits of such establishments may be observed and controlled in a multivariate econometric cost-function model. However, a sizable amount of such traits, such as leadership- and staff-level motivation, existing culture that drives patient-provider relationships, the level of access to external support, etc., may remain unobserved by the researcher. This phenomenon – commonly known as “selective program acceptance” makes the multivariate regression estimates, obtained using the OLS technique, biased, requiring application of the 3SLS technique for estimation of the cost function. The empirical model in this research attempts to address the “selectivity” or the “endogeneity” issue with an application of the 3SLS technique to estimate the cost function and thereby extricate the true effect of PCMH on cost.

The 3SLS technique involves estimation of the following four equations:

$$y = \beta_{0} + \beta_{1} y_{1} + \beta_{21} q + \beta_{22} q^{2} + \delta_{11} y_{1} q + \delta_{12} y_{1} q^{2} + \beta_{31} f + \beta_{32} f^{2} + \sum\limits_{i = 4}^{k} {\beta_{4} x_{i} + } \varepsilon_{1}$$

(A1)

$$y_{1} = \alpha_{0} + \alpha_{11} r + \alpha_{12} r^{2} + \alpha_{21} f + \alpha_{22} f^{2} + \sum\limits_{i = 1}^{50} {\alpha_{3i} } \,statedummy_{i} + \varepsilon_{2}$$

(A2)

$$y_{1} q = \theta_{0} + \theta_{11} r + \theta_{12} r^{2} + \theta_{21} f + \theta_{22} f^{2} + \sum\limits_{i = 1}^{50} {\theta_{3i} } \,statedummy_{i} + \varepsilon_{3} .$$

(A3)

$$y_{1} q^{2} = \gamma_{0} + \gamma_{11} r + \gamma_{12} r^{2} + \gamma_{21} f + \gamma_{22} f^{2} + \sum\limits_{i = 1}^{50} {\gamma_{3i} } \,statedummy_{i} + \varepsilon_{4}$$

(A4)

where.

y: average cost, which is either medical cost per medical visit or total cost per patient, it is either in logarithmic form or in linear form.

y₁: PCMH status = 1, if the health center is PCMH-recognized, = 0, if not,

q: either total number of medical visits, or total number of patients served, in a year,

f: total FTE,

x: set of all exogenous variables used as control,

r: total revenue,

Statedummy: represents 50 state dummies, where the state Wyoming is left out of the regression and kept as the reference category,

$\varepsilon_{1}$, $\varepsilon_{2}$, $\varepsilon_{3}$, and $\varepsilon_{4}$: represent error terms,

$\alpha$, $\beta$, $\gamma$, and $\theta$: represent slope parameters of the system of equations.

The variables $y$, $y_{1}$, $y_{1} q$, $y_{1} q^{2}$ are endogenous variables, all other variables are treated as exogenous to the system. The exogenous instrumental variables are the ones that are not included in the primary equation (A1). Specifically, the variable representing total revenue it square, and all the state dummies represent instrumental variables in the above system.

The variable “total revenue” serves as a good instrumental variable in the cost-function estimation, since higher revenue is associated with a larger size of the practice establishment and consequently, it can be highly correlated with the PCMH status. At the same time, because of the exclusion restriction provided by the economic theory, it cannot be a determinant of cost.²⁴ However, in order to make the instrument more powerful, instead of using the total revenue for the year 2014, we take the average of the total revenue pertaining to year 2014 and the three immediately prior years. The state-specific dummies in the three equations are also powerful exogenous instruments. They represent many unobserved factors that affect participation of the PCMH program, such as the prevailing scope-of-practice laws, unobserved cultural and socioeconomic factors that determine a health center’s decision to participate in the PCMH initiative. This makes state dummies as a group and the PCMH status highly correlated, as desired. On the other hand, since we already have the cost figures regionally adjusted using Geographic Price Cost Indices, there will be very weak association between costs and state dummies, as desired.

The exogenous variables, total FTE and its square deserve special mention as they appear on both primary cost equation as well as in the other three equations. Total FTE reflects the size of the establishment and thus, it can affect the average cost. Also, since large size establishments are more likely to have the PCMH status, total FTE is a determinant of the PCMH status. Moreover, among the practice establishments with the PCMH status there can be relative inefficiencies as it takes a long time to take the full impact of the PCMH to kick in. Thus, it is possible that the average cost will increase with the size of the establishment, as measured by total FTE, but at a decreasing rate. Therefore, we expect the coefficient on the variable total FTE to be positive, but the coefficient on its square to be negative in the primary equations of the “Visit Model” as well as the “Patient Model”.

Economies of scale

Slope of the average cost $= \frac{\partial y}{{\partial q}} = \beta_{21} + 2\beta_{22} q + \delta_{11} y_{1} + 2\delta_{12} y_{1} q$.

If $y_{1} = 1$, that is, if the health center has the PCMH status:

$$\text{Slope of the average cost }= \frac{\partial y}{{\partial q}} = (\beta_{21} + \delta_{11} ) + 2(\beta_{22} + 2\delta_{12} )q.$$

(A5)

If $y_{1} = 0$, that is, if the health center does not have the PCMH status:

Slope of the average cost

$$= \frac{\partial y}{{\partial q}} = \beta_{21} + 2\beta_{22} q.$$

(A6)

A negative slope of the average cost curve in (A5) and (A6) will reflect economies of scale.

Service provided at the lowest average cost

The lowest average cost occurs when the U-shaped average cost curve has slope zero.

If $y_{1} = 1$, that is, if the health center has the PCMH status, lowest cost occurs when

$$\frac{\partial y}{{\partial q}} = (\beta_{21} + \delta_{11} ) + 2(\beta_{22} + 2\delta_{12} )q = 0 \Rightarrow q = - (\beta_{21} + \delta_{11} )/2(\beta_{22} + 2\delta_{12} )q.$$

(A7)

If $y_{1} = 0$, that is, if the health center does not have the PCMH status, lowest cost occurs when

$$\frac{\partial y}{{\partial q}} = \beta_{21} + 2\beta_{22} q = 0 \Rightarrow q = - \beta_{21} /2\beta_{22} q.$$

(A8)

The expressions (A7) and (A8) are utilized in the study to compute the number of medical visits and the number of patients served at the lowest cost.

Computation of marginal effects

The pure PCMH effect can be obtained using the following steps:

Step 1: Plug in the value of $y_{1} = 1$ and in the cost function, keeping all else the same.

Step 2: Plug in the value of $y_{1} = 0$ and in the cost function, keeping all else the same.

Step 3: Subtract the value of the cost function obtained in step 2 from the that in step 1.

Step 1:

$$y\,(y_{1} = 1) = \beta_{0} + \beta_{1} + \beta_{21} q + \beta_{22} q^{2} + \delta_{11} q + \delta_{12} q^{2} + \beta_{31} f + \beta_{32} f^{2} + \sum\limits_{i = 4}^{k} {\beta_{4} x_{i} }.$$

(A9)

Step 2:

$$y\,(y_{1} = 0) = \beta_{0} + \beta_{21} q + \beta_{22} q^{2} + \beta_{31} f + \beta_{32} f^{2} + \sum\limits_{i = 4}^{k} {\beta_{4} x_{i} }.$$

(A10)

Subtracting (A10) from (A9) yields the pure effect of PCMH as follows:

Step 3:

$$\text{Pure Effect of PCMH}= \beta_{1} + \delta_{11} q + \delta_{12} q^{2}.$$

(A11)

The expression (A11) is used to compute the cost impact of PCMH for the 2014 data.

Simulation Steps

Multiply $q$ (patient population) by 1.10, 1.20, 1.30,……, 1.90, and 2.00 in the expression (A11) in order to obtain the pure effect of PCMH for a hypothetical 10%, 20%, 30%,……, 90%, and 100% increase, respectively, in the “Patient Model”.